Role of length polydispersity in the phase behavior of freely rotating hard-rectangle fluids

Abstract

We use the density-functional formalism, in particular the scaled-particle theory, applied to a length-polydisperse hard-rectangle fluid to study its phase behavior as a function of the mean particle aspect ratio κ_{0} and polydispersity Δ_{0}. The numerical solutions of the coexistence equations are calculated by transforming the original problem with infinite degrees of freedoms to a finite set of equations for the amplitudes of the Fourier expansion of the moments of the density profiles. We divide the study into two parts. The first one is devoted to the calculation of the phase diagrams in the packing fraction η_{0}-κ_{0} plane for a fixed Δ_{0} and selecting parent distribution functions with exponential (the Schulz distribution) or Gaussian decays. In the second part we study the phase behavior in the η_{0}-Δ_{0} plane for fixed κ_{0} while Δ_{0} is changed. We characterize in detail the orientational ordering of particles and the fractionation of different species between the coexisting phases. Also we study the character (second vs first order) of the isotropic-nematic phase transition as a function of polydispersity. We particularly focus on the stability of the tetratic phase as a function of κ_{0} and Δ_{0}. The isotropic-nematic transition becomes strongly of first order when polydispersity is increased: The coexistence gap widens and the location of the tricritical point moves to higher values of κ_{0} while the tetratic phase is slightly destabilized with respect to the nematic one. The results obtained here can be tested in experiments on shaken monolayers of granular rods.

Liquid crystals of hard rectangles on flat and cylindrical manifolds

“…[22][23][24][25][26][27][28][29][30] Moreover, dating back to the seminal work of Onsager, 31 these systems have been studied extensively by the density functional theory of freezing (DFT). 24,30,[32][33][34][35][36][37][38][39][40][41][42][43][44][45] Although most studies on liquid crystals of hard particles are performed in three spatial dimensions, twodimensional systems have been considered extensively as well. 25,26,30,[33][34][35]37,39,41,46,47 In two dimensions, the phase behavior is often more subtle: Even in the isotropic limit of hard disks, the crystallization transition is much more complex 48,49 than in the three-dimensional counterpart being hard-sphere freezing.…”

“…We do this for a two-dimensional system of hard rectangles and first study its bulk phase behavior in the flat and field-free case as a function of the particles' aspect ratio and number density. To tackle this problem, we propose a new DFT and perform complementary Monte Carlo (MC) computer simulations, showing stable isotropic, 34,47,59 nematic, 34,35,41,44,47,60 tetratic, [25][26][27][33][34][35]37,41,44,[60][61][62] and smectic 34,39,41,60 phases. Upon applying an aligning external field, the phase transition lines are shifted significantly and a binematic phase occurs at the expense of the tetratic phase.…”

Ordering, clustering, and wetting of hard rods in extreme confinement

“…From a 2D point of view, the confined rods can be considered as a polydisperse mixture of 2D hard discorectangles, where the polydispersity takes place in both length, due to the increase of orientational freedom, and diameter, due to the increase of out-of-plane positional freedom. The effect of polydispersity can be stronger for shorter rods, where the nature of 2D I-N transition changes from continuous to first order [45].…”

Uniform phases in fluids of hard isosceles triangles: One-component fluid and binary mixtures

“…At low aspect ratios the I phase can exhibit a direct transition to a plastic crystal (PK) or to a more complex crystalline phase in which particle shapes, orientations and lattice structures are coupled in a complex fashion. The phase behavior of HDR was studied in * Electronic address: yuri@math.uc3m.es † Electronic address: ardiaza@math.uc3m.es ‡ Electronic address: enrique.velasco@uam.es detail by MC simulations [1,2] and theory [2][3][4]. This particle shape, as well as the elliptical one [5][6][7], can stabilize the I, N, PK, and K phases with HDR exhibiting a region of S stability at high densities.…”